We calculate transition amplitudes and cross sections for excitation of hydrogen-like atoms by the twisted photon states, or photon states with more than one unit of angular momentum projection along the direction of propagation.
If the target atom is located at distances of the order of atomic size near the vortex center, the transitions rates into $l_f>1$ states become comparable with the rates for standard electric dipole transitions. It is shown that when the transition rates are normalized to the local photon flux, the resulting cross sections for $l_f>1$ are singular near the optical vortex center, i.e., high-multipole excitations take place in the region of zero field intensity near phase singularity. Relation to the "quantum core" concept introduced by Berry and Dennis is discussed.
Andrei Afanasev, Carl E. Carlson, and Asmita Mukherjee, "High-multipole excitations of atoms by twisted photons near phase singularity
(Conference Presentation)," Proc. SPIE 9922, Optical Trapping and Optical Micromanipulation XIII, 99220O (Presented at SPIE Nanoscience + Engineering: August 29, 2016; Published: 10 November 2016); https://doi.org/10.1117/12.2238828.5161498042001.
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